Immune networks: Multitasking capabilities near saturation

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Abstract

Pattern-diluted associative networks were recently introduced as models for the immune system, with nodes representing T-lymphocytes and stored patterns representing signalling protocols between T- and B-lymphocytes. It was shown earlier that in the regime of extreme pattern dilution, a system with N T T-lymphocytes can manage a number of B-lymphocytes simultaneously, with δ < 1. Here we study this model in the extensive load regime NB = αNT, with a high degree of pattern dilution, in agreement with immunological findings. We use graph theory and statistical mechanical analysis based on replica methods to show that in the finite-connectivity regime, where each T-lymphocyte interacts with a finite number of B-lymphocytes as NT → ∞, the T-lymphocytes can coordinate effective immune responses to an extensive number of distinct antigen invasions in parallel. As α increases, the system eventually undergoes a second order transition to a phase with clonal cross-talk interference, where the system's performance degrades gracefully. Mathematically, the model is equivalent to a spin system on a finitely connected graph with many short loops, so one would expect the available analytical methods, which all assume locally tree-like graphs, to fail. Yet it turns out to be solvable. Our results are supported by numerical simulations. © 2013 IOP Publishing Ltd.

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Agliari, E., Annibale, A., Barra, A., Coolen, A. C. C., & Tantari, D. (2013). Immune networks: Multitasking capabilities near saturation. Journal of Physics A: Mathematical and Theoretical, 46(41). https://doi.org/10.1088/1751-8113/46/41/415003

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